72 ANALYTICAL MKCHANK'ri PROBLEMS. 1. A weight of 5 tons is to be raised from the hold of a ship by means of a rope which takes 3| turns around the drum of a steam windlass. If At = 0.25 what force must a man exert at the other end of the rope? 2. By pulling with a force of 200 pounds a man just, keeps from surging a rope, which takes 2.5 turns around a post. Find the tensile force* at the other end of the rope, ju = 0-2. 3. A weight W is suspended by a rope which makes 1J turns around a clamped pulley and goes to the hand of a workman. If ju 0.2, find the force the man has to apply in order (a) to support the weight, (b) to raise it. 4. Two men, each of whom can exert a pull of 1250 pounds, can support a weight by means of a rope which takes 2 turns around a post. •On the other hand, one of the men can support it alone if the rope makes 2.5 turns. Find the weight. 5. In order to prevent surging a sailor has to exert a force of 150 pounds at the end of a hawser, which is used to keep (he .stern of a boat .at rest while the bow is being turned by the engines. Find flu* pull •exerted by the boat upon the hawser under the following conditions; [Hint. — Make use of equations (5) <nul ('!»),] (a)«-f. (b) fl = |, (c) 0 = |, (d) 0=T, (e) B-6-}, (f) 0 = Y' 6. A belt has to transmit an effective; fora- of ,r>(H) pounds, Find tin-tensile force on both sides of the bolt, under the following condition.*: (a) 8 = 135°, n = 0.5. (c) 0 -,- iiif)0, M - {).:>. (b) 6 = 135°, n = 0.4. (f) 0 ^ i,s(l", M , (),;{. (c) 0 = 150°, /i-0.3. (K) e - ING", At ».-,. (d) 6 = 165°, n = 0.5. (h) 0 - l!ir»°, p ()..j. 7. In the preceding problem find the width of the- hcli, .s.ippomng the permissible safe tensile force to be 50 pounds per inch of its width. = 0.2. (g) fl-ojr, = 0.5. (h) fl-Y' = 0.5, 0) e :,-. *f, = 0.4. (j) 0-:**, = 0.3. (k) 0 =, I:J= = f) 9. m ft ^w^